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THE CONSTRUCTION OF SUBORDINATED PROBABILITY MEASURES ON ℂ ASSOCIATED WITH THE JACOBI–SZEGÖ PARAMETERS

NOBUHIRO ASAI

Department of Mathematics, Aichi University of Education, Kariya, 448-8542, Japan

https://doi.org/10.1142/S0219025709003823Cited by:2 (Source: Crossref)

Abstract

In this paper, it will be shown that a probability measure on ℂ associated with the Jacobi–Szegö parameters of the orthogonal polynomials can be obtained by making use of the classical Mellin transform and its convolution property. We shall construct several measures on ℂ represented by the modified Bessel functions. The material in this paper gives nontrivial examples originated from the continuous dual Hahn polynomials (one of hypergeometric orthogonal polynomials), which are beyond the Meixner–Pollaczek polynomials appeared in our previous papers.^{4, 5}

Keywords:

AMSC: 44A15, 46L53

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